Problem: Reduce to lowest terms: $ \dfrac{6}{5} \div \dfrac{9}{2} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{9}{2}$ is $ \dfrac{2}{9}$ Therefore: $ \dfrac{6}{5} \div \dfrac{9}{2} = \dfrac{6}{5} \times \dfrac{2}{9} $ $ \phantom{ \dfrac{6}{5} \times \dfrac{2}{9}} = \dfrac{6 \times 2}{5 \times 9} $ $ \phantom{ \dfrac{6}{5} \times \dfrac{2}{9}} = \dfrac{12}{45} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{12}{45} = \dfrac{12 \div 3}{45 \div 3} = \dfrac{4}{15} $